(1) Field of the Invention
This invention relates to the field of sound generation by means of electronic instruments and computers equipped with appropriate sound generation devices.
In particular, music is produced by combination of sounds of different tones, or pitches, which can be characterized by fundamental physical frequencies of sound waves. Most conventional approaches to musical composition are based on providing a time sequence of such tones, which have their frequencies in a certain relation to each-other, that makes it pleasant to the ear. In particular, the relations characterized by simple ratios, such as 2, 1/2, 3/2, 3/4, 4/3, etc. are most pleasant. This could be related to resonances caused by such frequencies inside the ear, or some more complex phenomena inside the brain.
Indeed, the earlier instruments were based on resonating strings, and were tuned to follow these ratios, which is reflected, for example, in Pythagorean scale. However, those scales have a limitation that it is impossible to build a set of octaves from those scales, spanning several orders of magnitude of the base frequency. This is the reason why, most modern instruments are based on chromatic scale, which removes this limitation by sub-dividing an arbitrary range of frequencies into equal intervals on a logarithmic scale (FIG. 2, where number above each line added to one is equal to the scaling factor used to obtain the frequency associated with that line). But by moving to a logarithmic scale, one can no longer reproduce exact ratios for most of the tones. Thus, chromatic scale compromised the purity of tones to achieve a versatility of the instrument, which enabled the development of key-based instruments, such as piano, organ, or modern music keyboards.
Another method of musical composition is based on the idea of harmony, whereby a composition is subdivided into measures, and each measure is assigned to a specific harmonic scale, which is defined as a sequence of harmonic triads or keys, that are pleasant to the ear. The well known harmonic scales are major and minor scales. When combined into a sequence, harmonic scales form a harmonic sequence, which determines the character of a song. For example, the harmonic sequence “C” (C-major), “Am” (A-minor), “F” (F-major), and “G” (G-major) is common in many popular songs.
Along with harmonic sequences, another common practice is to apply a frequency shift in a form of modulation, or transposition. In the current invention these ideas are generalized to a method of hierarchical multi-scale composition. This method provides a procedure and an outline of an instrument, which overcome the limitations of both Pythagorean and chromatic scales by unifying harmonic sequencing and modulation as a general method of hierarchical composition. This invention also generalizes the idea of a musical scale to a multi-scale composition, or multi-scale orchestra of instruments.
When a single scale is used this method simplifies performing and writing of music as compared to chromatic scale. This is because it replaces a multitude of tonic combinations for every keys by a single scale, which is a set of basic ratios. For example, instead of remembering major/minor tonic triads for every key, such as “C,E,G”, “C,D#,G” for major/minor triads in C-key, etc. (total of 2*12=24 combinations), one will only remember two combinations of ratios: (1, 5/4, 3/2) for a major triad and (1, 6/5, 3/2) for a minor triad (and in fact, the first number is always 1). Shifting to different keys will amount to multiplication (modulation) of these numbers by a rational number selected from the scale used. For example, a sequence (1, 9/8, 5/4, 4/3, 3/2, 5/6, 15/8) will resemble the chromatic major scale. Shifting to different octaves amounts to multiplication by a power of 2.
(2) Description of Related Art Including Information Disclosed Under 37 CFR 1.97 and 1.98.                1. Deutsch (U.S. Pat. No. 4,697,490 A) is entitled “Musical tone generator using incremental harmonic variation”.        2. Van Buskirk (U.S. Pat. No. 5,684,260 A) is entitled “Apparatus and method for generation and synthesis of audio”.        3. Takeuchi (U.S. Pat. No. RE31653 E) is entitled “Electronic musical instrument of the harminic synthesis type”.        